Compartmental model identification based on an empirical Bayesian approach: the case of thiamine kinetics in rats

Compartmental models are a very popular tool for the analysis of experiments in living systems. There are three main aspects that have to be taken into account: the degree of detail of the model, its a priori identifiability and the a posteriori (numerical) identifiability. In some cases, where standard approaches are adopted, the models can be either a priori or a posteriori unidentifiable. The paper proposes model identification within a Bayesian framework, to solve a posteriori unidentifiability problems. In particular, a stochastic simulation algorithm is proposed to perform a Bayesian identification of compartmental models, and an empirical Bayesian technique is proposed to propagate information among multiple experiments. The power of this methodology was demonstrated by evaluating the kinetics of thiamine under several experimental conditions. The complexity of the existing model (nine parameters) and limited experimental data (8/12 for each model) caused a posteriori identifiability problems when standard approaches were adopted. The application of the methodology identifies all 28 models (four tissues under seven different conditions).